ANALYSIS OF THE BOUNDARY-CONDITION AT THE INTERFACE BETWEEN A VISCOUS-FLUID AND A POROUS-MEDIUM AND RELATED MODELING QUESTIONS

This paper deals with three fundamental modelling questions for the Da rcy and Brinkman equations for flow in a porous medium. It is first sh own that in the Dirichlet initial - boundary value problem for the Bri nkman equations the solution depends continuously on the viscous coeff icient. Then L-2 convergence of the solution of this problem to the so lution of an analogous problem for the Darcy equations is established. Finally, it is proved that for flow in a domain occupied by a viscous fluid in contact with a porous solid, the solution depends continuous ly on a coefficient in the interface boundary condition. The continuou s dependence holds for Stokes flow in the fluid, and the analogous Nav ier-Stokes situation is discussed. (C) Elsevier, Paris.